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arXiv · 1607.07843

Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results

Ziyang Gao
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Abstract

We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the Ax logarithmique theorem and the Ax-Lindemann theorem which we shall prove. We also prove the whole Ax-Schanuel conjecture for the unipotent part. All these bi-algebraic and transcendental results generalize their counterparts for mixed Shimura varieties. In the end we briefly discuss about the Andre-Oort and Zilber-Pink type problems for enlarged mixed Shimura varieties.

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Ziyang Gao. 2016-07-26. Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results. https://arxiv.org/abs/1607.07843

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